Blackwell's 54-ball half-century threatened to turn the tide but the visitors remained favourites when Hoggard had the left-hander caught behind for 64, prodding at a good length ball.
Raffaele Palladino made it 3-0 from the spot, while the visitors ended the game with nine men when Fabrizio Cacciatore was red-carded with two minutes left as tempers flared.
But they finally breached the visitors' defence with 14 minutes left when Brown finished off another onslaught after a dozen phases.
Pressman was a busy man in the visitors' net, saving again when Wrack drilled in a left-foot shot from near the edge of the box.
When Rikki Clarke hit two boundaries from the penultimate over, that left the visitors needing just eight to win from the final over.
The visitors should have scored in the first minute when a chip to the left found Dimitri Pelo, but the winger's pass inside was intercepted by Adey Gardner.
Referee Charlie Richmond played good advantage when one of the visitors was fouled, and the ball broke to McKay who left Morton goalkeeper Colin Stewart no chance with a raking drive inside the post.
The visitors took the lead after just four minutes when Mark Bentley netted with a fine left-foot effort from a Paul Sturgess cross.
The visitors had the game's first opening when Bobby Zamora found space on the left and, ignoring well-placed team-mates to his right, curled a shot well wide of the post.
The visitors looked to seal the match with a clinching goal four minutes later when McCulloch sent a left-foot shot wide.
The visitors took a deserved lead when Lee Martin played the ball across the penalty area from the left and Drury swept the ball into the bottom corner from 20 yards.
The visitors broke the deadlock in the 18th minute when Parkin rose to nod in a Craig cross and left Accies keeper Tomas Cerny stranded.
But the visitors responded with their second try when a wonderful bullet pass from Andy Farrell found Cato on the left wing to touch down on 64 minutes.
The visitors' lacklustre play was epitomised when a well-worked free-kick saw Nani play in Evra on the left only for his low whipped ball to fly across the Villa goalmouth without a team-mate showing a desire to get to it.
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